Magnetic stimulation is a new technique for activating neurons that is both painless and noninvasive. Stimulation occurs when a brief current pulse is passed through a coil placed near the neuron, producing an electric field by electromagnetic induction. The goal of this project is to develop mathematical models to calculate the electric field induced in the human body during magnetic stimulation. Two models are developed in detail: (1) a model of the stimulation of a peripheral nerve in the arm, and (2) a model of the stimulation of the brain. Techniques to solve the inverse problem of determining the appropriate coil geometry for producing a specified electric field distribution are also studied.